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Block #194,063

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2013, 9:51:13 PM Β· Difficulty 9.8782 Β· 6,615,471 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
b7f86b5966524ca24b7b6f79a3ef1fc227abe33656a72b09f519fbf9b6dd977c
View on Chainz β†—

Height

#194,063

Difficulty

9.878190

Transactions

2

Size

1.01 KB

Version

2

Bits

09e0d112

Nonce

8,751

Timestamp

10/4/2013, 9:51:13 PM

Confirmations

6,615,471

Mined by

⛏️ P2SHAKgCoh7CJFSvHNNuuLiHvAow1gLYsNGjDy

Merkle Root

4411b65d5bfe98ec3a469802e56658656217c784cedf9cbf0bdf72a1a087a430
Transactions (2)
Coinbase04932263318944…ca6e9d28902175
1 in β†’ 1 out10.2400 XPM109 B
AKgCoh7C…LYsNGjDy
168f62a347025a…ebfd463699bbcd
7 in β†’ 1 out71.6800 XPM840 B
ATV4M1CV…dd9zw8nH
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.719 Γ— 10⁹³(94-digit number)
17197257860732012876…54100196570947503361
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
1.719 Γ— 10⁹³(94-digit number)
17197257860732012876…54100196570947503361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.439 Γ— 10⁹³(94-digit number)
34394515721464025752…08200393141895006721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.878 Γ— 10⁹³(94-digit number)
68789031442928051504…16400786283790013441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.375 Γ— 10⁹⁴(95-digit number)
13757806288585610300…32801572567580026881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.751 Γ— 10⁹⁴(95-digit number)
27515612577171220601…65603145135160053761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.503 Γ— 10⁹⁴(95-digit number)
55031225154342441203…31206290270320107521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.100 Γ— 10⁹⁡(96-digit number)
11006245030868488240…62412580540640215041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.201 Γ— 10⁹⁡(96-digit number)
22012490061736976481…24825161081280430081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.402 Γ— 10⁹⁡(96-digit number)
44024980123473952963…49650322162560860161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,720,351 XPMΒ·at block #6,809,533 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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